The case of a small number of anti-branes or actually a single anti-brane (potentially placed on top of an O-plane) has also been studied extensively in the last few years [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}. This is particularly important for our discussion here since in this case the connection between the VA action for the goldstino and the anti-D3-brane worldvolume fields has been made manifest (see also [15]} for a generalization to multiple anti-branes). So, we will from now on mostly focus on the case of a single anti-D3-brane.It was shown in [16]} that multiple anti-D3-branes seem to repel each other. Given that they are confined to the bottom of a warped throat in KKLT type constructions, this might then justify the study of each of them as a single anti-D3-brane, even when multiple anti-D3-branes are present [1]}. For a single anti-brane in a flux background the authors of [1]} argue that one should include the anti-D3-brane action (that contains the VA action) as part of the low energy field theory, which is what has been done so far in the literature and also in [19]}. However, the authors of [1]} find no instability in this setup and show that divergences in the flux cloud near the anti-brane get resolved by matching onto string theory at short distances. Furthermore, the authors of [1]} show that the only allowed anti-D3-brane instability is the NS5-brane instanton described by KPV [22]}. As mentioned above this decay channel has been studied in great depth and in particular from the stand point of non-linear supersymmetry in [11]}, [13]}. There exists now universal agreement in the literature that there are metastable vacua after the polarization of the anti-D3-branes into an NS5-brane. As stated in [19]}, the connection of their instability to the KPV paper is unclear, so it could be that their result is related to the polarization of anti-D3-branes into a metastable NS5 brane. However, at least for a single anti-D3-brane the claims in [19]} seem to be at odds with the perturbative stability that was observed in [1]} via a more explicit study of an anti-D3-brane in a flux background.
